No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers.

The Heisenberg limit to laser coherence C-the number of photons in the maximally populated mode of the laser beam-is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's Q=0). We then show that the relation between C and sub-Poissonianity (Q<0) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semiunitary gain (which allows Q→-1), and random (Markovian) pumping with optimized gain, C is maximized when Q is minimized.

Thermodynamics from first principles: Correlations and nonextensivity.

The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this Rapid Communication, we use the fundamental principles of ergodicity (via Liouville's theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting systems. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.

Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks.

Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices can lead to finite energies per site, which deserves attention. Here, we present a tensor network approach to construct the ground states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on constrained optimizations of their infinite matrix product states description, which contains no truncation step, offers a very simple mathematical structure, and other minor advantages at the cost of slightly higher polynomial complexity in comparison to an existing method. More precisely speaking, our proposed algorithm is in part equivalent to the more generic and well-established solvers of infinite density-matrix renormalization-group and variational uniform matrix product states, which are, in principle, capable of accurately representing the ground states of such infinite-range-interacting many-body systems. However, we employ some mathematical simplifications that would allow for efficient brute-force optimizations of tensor-network matrices for the specific cases of highly-symmetric infinite-size infinite-range models. As a toy-model example, we showcase the effectiveness and explain some features of our method by finding the ground state of the U(1)-symmetric infinite-dimensional antiferromagnetic XX Heisenberg model.